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Questions and Answers
If the hypotenuse of a right triangle is 28 and the length of the side opposite to angle 𝜃 is 17, what is the measure of angle 𝜃?
What is the value of x if the adjacent side is 8 and the angle is 34° in a right triangle?
Which expression accurately factors 6𝑥² − 18𝑥 − 24 after factoring out the GCF?
If triangle ABC is similar to triangle DEF and AB = 9, DE = 16, and BC = 5, what is the length of EF?
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In an isosceles triangle with base angles measuring 2𝑥 + 4° and 𝑥 + 36°, what is the value of x?
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Study Notes
Right Triangle Calculations
- A right triangle has one 90-degree angle
- To solve for missing variables in right triangles, use trigonometric functions: sine, cosine, and tangent.
- Sine (sin) = Opposite side / Hypotenuse
- Cosine (cos) = Adjacent side / Hypotenuse
- Tangent (tan) = Opposite side / Adjacent side
- Use the inverse trigonometric functions (arcsin, arccos, arctan) to find the angle.
Factoring Algebraic Expressions
- Factoring involves breaking down an expression into the product of its factors.
- Greatest Common Factor (GCF): Find the largest factor common to all terms in the expression and factor it out.
- Factoring Quadratics: For an expression in the form of ax^2 + bx + c, find two numbers whose product is ac and whose sum is b.
- Difference of Squares: A difference of squares is factored as (a + b)(a - b), where a and b are square roots of the squared terms.
Similar Triangles
- Similar triangles have the same shape but different sizes.
- Corresponding angles are equal.
- Corresponding sides are proportional.
- If two triangles are similar, the ratio of corresponding sides is constant.
Probability and Area Model
- Probability is the likelihood of an event occurring.
- Area Model: A visual representation of probabilities using a grid.
- Probability of "And": Multiply the probabilities of the individual events.
- Probability of "Or": Add the probabilities of the individual events, subtracting any overlap.
Isosceles Triangles
- An isosceles triangle has two equal sides and two equal angles.
- The angles opposite the equal sides are also equal.
- The sum of the interior angles of a triangle is 180 degrees.
- Use this information to solve for the missing angles in an isosceles triangle.
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Description
This quiz covers essential concepts in right triangle calculations, including trigonometric functions and their inverses. It also discusses factoring algebraic expressions, focusing on methods like Greatest Common Factor and factoring quadratics. Test your knowledge on these vital mathematical principles!
